Determining extracellular analyte concentration with nanoplasmonic sensors

ABSTRACT

Methods and systems for determining extracellular concentration data of an analyte are disclosed. A method for determining extracellular concentration data of an analyte includes receiving sensor data from one or more arrays of functionalized plasmonic nanostructures on a localized surface plasmon resonance imaging chip in contact with a fluid containing at least one living cell for a plurality of times, determining intensity data for the one or more arrays, determining fractional occupancy based on the intensity data, and determining extracellular concentration data based on the fractional occupancy data. A system for determining extracellular concentration data of an analyte includes a LSPRi chip, a sensor component, an intensity component, a fractional occupancy component, a concentration component, and a processor to implement the components.

This application claims the benefit of U.S. Provisional Application No.62/181,939, filed on Jun. 19, 2015 by Marc P. Raphael et al., entitledIMAGING EXTRACELLULAR PROTEIN CONCENTRATION WITH NANOPLASMONIC SENSORS,the disclosure of which is incorporated herein by reference, in itsentirety.

BACKGROUND

Aspects of the exemplary embodiment relate to detection of analytes in afluid and find particular application in connection with the detectionof extracellular proteins using nanoplasmonic sensors.

From bacterium to eukaryote, a cell's fate is directly tied to its localchemical environment. The measurement of external protein concentrationsand gradients by membrane bound receptors is useful in the study of celldifferentiation, motility and proliferation. Such dependencies have beendeduced by introducing artificial gradients to cell cultures. However,direct measurements of the spatio-temporal concentrations of analytes,which cells themselves produce via secretion, have remained elusive.

One roadblock has been the lack of an assay that can measureextracellular protein concentrations in real time without disrupting thesignaling pathways of interest. This real time, non-invasive requirementseverely limits the techniques that can be employed, including commonfluorescent labeling methods. For example, while fluorescent fusionproteins have been useful in the study of intracellular proteinmeasurements, the technique does not lend itself to extracellularsignaling. A tag, such as green fluorescent protein (GFP) tag of about27 kDa, for example, may compromise the labeled protein's ability tonavigate the complexities of the secretory pathway (Wiedenmann et al.,“Fluorescent Proteins for Live Cell Imaging: Opportunities, Limitations,and Challenges,” lubmb Life 61(11):1029-1042 (2009); Costantini, et al.,“Fluorescent Proteins in Cellular Organelles: Serious Pitfalls and SomeSolutions,” DNA Cell Biol. 32(11):622-627 (2013)).

Even if the proteins are successfully secreted, the result is a diffusefluorescent glow outside the cell which is difficult to quantify.Fluorescently-labeled antibodies used for immunosandwich assays havebeen successfully introduced outside of live cells to measure secretions(Bailey, et al., “DNA-encoded antibody libraries: A unified platform formultiplexed cell sorting and detection of genes and proteins,” J. Am.Chem. Soc. 129(7):1959-1967 (2007); Han, et al., “Polyfunctionalresponses by human T cells result from sequential release of cytokines,”Proc. Natl. Acad. Sci. U.S.A. 109(5):1607-1612 (2012); Shirasaki, etal., “Real-time single-cell imaging of protein secretion,” ScientificReports 4 (2014)). However, the addition of these relatively largeprobes (typically 150 kDa) is an impediment to downstream signaling andthe techniques typically involve isolating individual cells. In bothexamples, the ability to establish causal relationships between secretedprotein concentrations and cell fate, whether the signaling beautocrine, paracrine or endocrine in nature, is hampered by the probesthemselves.

Solid-state nanosensors have the potential to overcome this impasse.Probes such as nanodiamonds and metallic nanostructures arebiocompatible, do not suffer from photobleaching and, advantageous fromthe protein secretion perspective, are label-free techniques.Nanodiamond sensors are highly sensitive magnetic field detectorsresulting from nitrogen vacancies, which makes the techniqueparticularly applicable to detecting metalloproteins (Horowitz, et al.,“Electron spin resonance of nitrogen-vacancy centers in opticallytrapped nanodiamonds,” Proc. Natl. Acad. Sci. USA. 109(34):13493-13497(2012); Ermakova, et al., “Detection of a Few Metallo-Protein MoleculesUsing Color Centers in Nanodiamonds,” Nano Lett. 13(7):3305-3309(2013)). Metallic nanoparticles exhibit a localized surface plasmonresonance (LSPR) which is sensitive to changes in the local refractiveindex of the surrounding medium. Their surfaces can be biofunctionalizedfor the detection of proteins, lipids, and DNA in cell-free environments(Sepulveda, et al., “LSPR-based nanobiosensors,” Nano Today 4(3):244-251(2009); Mayer, et al., “A single molecule immunoassay by localizedsurface plasmon resonance,” Nanotechnology 21(25) (2010); Haes, et al.,“A nanoscale optical blosensor: Sensitivity and selectivity of anapproach based on the localized surface plasmon resonance spectroscopyof triangular silver nanoparticles,” J. Am. Chem. Soc.124(35):10596-10604 (2002); Nusz, et al., “Label-free plasmonicdetection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4):984-989 (2008); Jonsson et al., “Supported lipid bilayer formationand lipid-membrane-mediated biorecognition reactions studied with a newnanoplasmonic sensor template,” Nano Lett. 7(11):3462-3468 (2007);Dahlin, et al., “Specific self-assembly of single lipid vesicles innanoplasmonic apertures in gold,” Adv. Mater. 20(8):1436-1422 (2008);Endo, et al., “Label-free detection of peptide nucleic acid-DNAhybridization using localized surface plasmon resonance based opticalbiosensor,” Anal. Chem. 77(21):6976-6984 (2005); Lo, et al., “Monitoringof DNA-protein interaction with single gold nanoparticles by localizedscattering plasmon resonance spectroscopy,” Methods 64(3):331-337(2013)). In addition, LSPR optical configurations are readily integratedwith standard wide-field microscopy setups which have enabled thedetection of protein secretions in the presence of thousands of cells,as well as real-time single cell secretions (Oh, et al. “IntegratedNanoplasmonic Sensing for Cellular Functional Immunoanalysis Using HumanBlood,” ACS Nano 8(3):2667-2676 (2014); Endo et al., “Label-freecell-based assay using localized surface plasmon resonance biosensor,”Anal. Chim. Acta 614(2):182-189 (2008); Raphael et al., QuantitativeImaging of Protein Secretions from Single Cells in Real Time. Biophys.J. 105(3):602-608 (2013)). However, measuring extracellular proteinconcentrations in both space and time, for modeling and quantifying ofsignaling pathways, has remained a challenge (Kolitz, et al.,“Measurement and Modeling of Signaling at the Single-Cell Level,”Biochemistry 51(38):7433-7443 (2012)).

Additionally, methods using spectrometry-based techniques are severelyrestrictive in that they only allow for a single array's response to bequantified, and the spectrometer requires a lot of light and significantexposure time, which could be harmful to live cells.

Thus, it would be desirable to have a method and system for measuringextracellular analyte concentrations in space and time, without the needfor use of fluorescent tagging and without the need to use aspectrometer.

INCORPORATION BY REFERENCE

The following references, the disclosures of which are incorporatedherein by reference in their entireties, are mentioned.

U.S. Pub. No. 2014/0273002, published Sep. 18, 2014, entitledNANOSPLASMONIC IMAGING TECHNIQUE FOR THE SPATIO-TEMPORAL MAPPING OFSINGLE CELL SECRETIONS IN REAL TIME by Marc P. Raphael, et al.

U.S. Pub. No. 2014/0095100, published Apr. 3, 2014, entitled CALIBRATINGSINGLE PLASMONIC NANOSTRUCTURES FOR QUANTITATIVE BIOSENSING by Marc P.Raphael, et al.

U.S. Pub. No. 2014/0093977, published Apr. 3, 2014, entitled LIGHTMICROSCOPY CHIPS AND DATA ANALYSIS METHODOLOGY FOR QUANTITATIVELOCALIZED SURFACE PLASMON RESONANCE (LSPR) BIOSENSING AND IMAGING byMarc P. Raphael, et al.

BRIEF DESCRIPTION

In accordance with one aspect of the exemplary embodiment, a method fordetermining extracellular concentrations of an analyte includesreceiving sensor data from one or more arrays of functionalizedplasmonic nanostructures on a localized surface plasmon resonanceimaging (LSPRi) chip in contact with a fluid containing at least oneliving cell for a plurality of times. Intensity data is determined forthe nanostructures, based on the sensor data for each of the pluralityof times. fractional occupancy data is determined for thenanostructures, based on the intensity data for each of the plurality oftimes. Extracellular concentration data of the analyte is determined,based on the fractional occupancy data for each of the plurality oftimes.

One or more of the steps of the method may be performed with aprocessor.

In accordance with another aspect of the method, the method may furthercomprise determining movement of the analyte in the fluid from theextracellular concentration data by mapping the extracellularconcentration data of the analyte for the LSPRi chip.

In accordance with another aspect of the exemplary embodiment, acomputer-implemented system for determining extracellular concentrationsof an analyte includes a localized surface plasmon resonance imaging(LSPRi) chip, a sensor component for receiving sensor data for aplurality of times, an intensity component that determines imageintensity data based on the sensor data for the plurality of times, afractional occupancy component that determines fractional occupancy databased on the intensity data for each of the plurality of times, and aconcentration component that determines extracellular concentration databased on the fractional occupancy data for each of the plurality oftimes. The LSPRi chip includes a substrate and one or more arrays offunctionalized plasmonic nanostructures formed on the substrate. Eacharray is in contact with a fluid containing at least one living cell. Aprocessor implements the components.

In accordance with another aspect of the exemplary embodiment, a methodof determining extracellular concentrations of an analyte in a fluidincludes providing at least one array of functionalized plasmonicnanostructures on a localized surface plasmon resonance imaging (LSPRi)chip in contact with a fluid containing at least one living cell. Foreach of a plurality of times, sensor data is received from one or moreof the arrays of functionalized plasmonic nanostructures. Fractionaloccupancy data is determined for the nanostructures based on the sensordata for each of the plurality of times. Extracellular concentration ofthe analyte is spatially and temporally mapped, based on the fractionaloccupancy data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a portion of an apparatus used tomeasure extracellular concentrations of an analyte according to oneaspect of the exemplary embodiment;

FIG. 2 is top plan view of a LSPRi chip according to another aspect ofthe exemplary embodiment;

FIG. 3 is a top plan view of an array of nanostructures in the LSPR chipof FIG. 2;

FIG. 4 is a side sectional view of functionalized nanostructures in theLSPR chip of FIG. 2;

FIG. 5 is a functional block diagram of a computer-implemented systemfor measuring extracellular concentrations of an analyte in a liquidmedium according to another aspect of the exemplary embodiment;

FIG. 6 is a flow chart illustrating a method for measuring extracellularconcentrations of an analyte in accordance with another aspect of theexemplary embodiment;

FIG. 7 is a graph of normalized image intensity vs time for theexemplary CCD camera;

FIG. 8 is a graph of normalized image intensity vs fractional occupancyobtained in three experiments;

FIGS. 9-11 schematically illustrate data analysis for determiningconcentration form fractional occupancy, where FIG. 9 illustratessubsampling of fractional occupancy over time; FIG. 10 illustrates anenlarged portion of the plot of FIG. 9, and FIG. 11 is a plotillustrating each linear model as a point in a plane;

FIG. 12 is a graph of a piece-wise function of three simulatedtime-dependent concentration scenarios: a gradual increase; a sharpincrease; and a sharp decline, vs time in determining extracellularconcentrations from simulated data;

FIG. 13 is a graph of fractional occupancy vs time in determiningextracellular concentrations from simulated data, with simulatedGaussian noise;

FIG. 14 is a graph of fractional occupancy vs time in determiningextracellular concentrations from simulated data with local linearmodels fitted to the data;

FIG. 15 is a graph of simulated extracellular concentration vs time;

FIG. 16 is a photograph of an LSPR chip during the quantification ofextracellular concentrations with steady-state secretions of a protein;

FIG. 17 is a graph of fractional occupancy vs time for two local arraysin the LSPR chip of FIG. 16;

FIG. 18 is a graph of calculated extracellular concentration data forthe local arrays of FIG. 16, after applying a temporal filter;

FIG. 19 is a photograph of an LSPR chip during the quantification ofextracellular concentrations with burst secretions of a protein;

FIG. 20 is a graph of fractional occupancy vs time for the labeledarrays in the LSPR chip of FIG. 19;

FIG. 21 is a graph of calculated extracellular concentration data forthe labeled arrays of FIG. 19, after applying a temporal filter;

FIG. 22 is a graph of determined concentration for a local array of FIG.16 two different time windows; and

FIG. 23 is a graph of the signal to noise ratio with varying timewindow.

DETAILED DESCRIPTION

Methods and systems for measuring extracellular concentrations of ananalyte are disclosed wherein single cell secretions may be imaged overtime and spatial distance from one or more biological cells. Thetechnique is useful for determining the flow of analytes, such asproteins, lipids, and DNA, in a liquid medium.

In embodiments disclosed herein, arrays of gold plasmonic nanostructuresare used for real-time imaging of secreted protein concentrations. Theinference of concentration from nanoplasmonic imagery is assisted by twotechniques. First, when normalized, LSPR imagery (LSPRi) can be used todetermine the fraction of active surface ligands bound to the analyte(fractional occupancy). Second, to calculate concentration, an analysisapproach is used which is based on temporal filtering that utilizes theLSPRi-determined fractional occupancy and reaction rate constants asinputs. Applying this approach to the spatio-temporal mapping ofsecreted antibody concentrations from hybridoma cells, single cellsecretions can be imaged with a time resolution of 15 seconds over aspatial range extending 130 μm from the center of the cell. Sensingarrays located next to individual cells resolved steady-stateconcentrations between 0.2 and 1.3 nM. Burst-like secretions can also bemeasured in which the transient concentration reaches as high as 56 nMover the course of several minutes and then dissipates. The ability tomeasure secreted concentrations with high spatial and temporalresolution has applicability to numerous analytes and cell types.

With reference to FIG. 1, an illustration of a detection system 1 usedto measure extracellular concentrations of an analyte in a liquid mediumaccording to one aspect of the exemplary embodiment is shown. Thedetection system 1 includes an apparatus 10, which includes: an LSPRichip 12, which includes a light-transmitting substrate 14, such as aglass coverslip, which is patterned with a plurality of nanostructures16, which may be arranged in one or more arrays. The glass coverslip maybe of the type conventionally used in a standard light microscope.

A chamber 18, mounted on the substrate 14, holds a liquid medium 20,which is in contact with the nanostructures 16. The liquid medium maycontains one or more living cells. An objective lens 22 is positionedadjacent the substrate to receive emissions from the nanostructurespassing therethrough. A charge coupled device (CCD) 24, such as a CCDcamera, is positioned to receive inputs from the lens. In particularembodiments, the apparatus 10 may include one or more of: beam splitters25, 26, a linear polarizer 27, a crossed linear polarizer 28, and amirror 30. Other detection devices, such as a spectrometer 31, mayoptionally be included. In use, the excitation light from a visiblelight source 35, such as a halogen lamp, passes through the linearpolarizer 27 and illuminates the arrays 34 through the objective lens22. Photons emitted by the nanostructure are collected by the objectivelens 22, passed through the crossed linear polarizer 28 and reflected bymirror 30 to CCD camera (labeled CCD). Optionally, a beam splitter 31,intermediate the mirror 30 and CCD, allows some of the energy (reflectedlight) to enter the spectrometer 31. Alternatively, the spectrometer 31is omitted from the system 1. Sensor data 32 from the detectiondevice(s) 24, 31 are sent to a processing system 33, which is describedin greater detail with reference to FIG. 5.

With reference to FIG. 2, a top view of an exemplary LSPRi chip 12 isshown. The LSPRi chip 12 includes one or more arrays 34 ofnanostructures. In the embodiment illustrated in FIG. 2, twelve arrays34 of plasmonic nanostructures 16 are shown. In particular embodiments,the coverslip 14 is patterned via electron beam lithography toincorporate arrays 34 of plasmonic nanostructures 16, which may beformed predominantly of gold. One or more live cells 36 are located inthe liquid medium, in proximity to the coverslip 14 and the arrays 34 ofnanostructures 16.

With reference one again to FIG. 1, the arrays 34 are illuminated with asource 35 of visible illumination, such as a 100 W halogen lamp. Thepolarizers 26, 28 may be used to minimize background contributions fromlight scattered by the glass substrate.

With reference also to FIG. 3, a single array 34 of nanostructures 16 isshown. Each nanostructure 16 may be at least 10 nm, or at least 20 nm,or up to 200 nm, or up to 100 nm, or up to 250 nm, in diameter, and atleast 20 nm, or at least 50 nm, or up to 500 nm, or up to 200 nm, inheight. In specific embodiments, the nanostructures 16 may be 70-80,e.g., 75 nm in diameter and 60-100, e.g., 80 nm in height.

The nanostructures 16 may be arranged in different patterns, such as ann×m array 34, where each of n and m is at least 5, such as up to 50. Forexample, as shown in FIG. 3, the nanostructures 16 may be arranged in a20×20 array 34. In particular embodiments, the nanostructures 16 may bespaced from 200 to 1000 nm apart, center-to-center, which thus definesthe pitch range. The nanostructures 16 may have thus a pitch of 300-500nm. The arrays 34 may have a pitch of at least 5 μm, or at least 20 μm,such as at least 30 μm, or up to 100 μm, or up to 40 μm, e.g., 33 μm asmeasured from their respective centers.

The arrays 34 may have a resonance peak centered at 250-800 nm. In someembodiments, the arrays 34 may have a resonance peak centered at about635 nm in aqueous media.

Methods for forming the arrays of nanostructures are described, forexample, in above-mentioned U.S. Pub. Nos. 2014/0273002, 2014/0095100,and 2014/0093977, incorporated herein by reference

With reference to FIG. 4, an enlarged side sectional view of a portionof the LSPRi chip 12 is shown, with two functionalized nanoplasmonicstructures 16. The nanostructures 16 may be functionalized with ligands38 that are able to bind a specific target analyte 40 in the liquidmedium. For example, the nanostructures 16 may be biologicallyfunctionalized by first applying a two-component self-assembledmonolayer of first and second thiols in a 3:1 ratio. The majority(first) thiol component may be terminated with polyethylene glycol toprevent non-specific binding while the minority (second) componentterminates with an amine group (or other functional binding group) forcovalent ligand attachment.

The analyte 40 may be a protein, such as an antibody, secreted by one ormore cells 36 contained within the fluid 20 of the chamber 18. Analyte40 binding to the ligands 38 causes a perturbation in the local index ofrefraction of the plasmonic nanostructures 16, which is manifested as aspectral red shift and increase in intensity. When imaged by the CCDcamera, the arrays 34 are observed to brighten with increasing spectralshift (i.e., increased binding). A known analyte 40 (e.g., commerciallyobtained in high purity) may be used to normalize the spectral responseof the arrays 34 of functionalized nanostructures 16, e.g., aftertesting

In particular embodiments, the configuration of the apparatus 10integrates with traditional cell microscopy techniques, such asfluorescence and/or brightfield imaging, which may be accessible by theautomated switching of a filter cube (not shown).

With reference to FIG. 5, a functional block diagram of acomputer-implemented sensor data processing system 33 for determiningextracellular concentration data of an analyte is shown. The illustratedcomputer system 33 includes memory 54 which stores software instructions56 for performing the method illustrated in FIG. 6 and a processor 58 incommunication with the memory for executing the instructions 56. Thesystem 33 also includes one or more input/output (I/O) devices 60, 64,such as a network interface and a user input output interface. The I/Ointerface 64 may communicate with one or more displays, for displayinginformation to users, and a user input device, such as a keyboard, ortouch or writable screen, and/or a cursor control device, such as mouse,trackball, or the like, for inputting text and for communicating userinput information and command selections to the processor device 58. I/Ointerface 60 receives sensor data 32 from the detection device(s) 24,31. The various hardware components 54, 58, 60, 64 of the processingsystem 33 may all be connected by a data/control bus 65.

The data processing system 33 may include one or more computing devices,such as a PC, such as a desktop, a laptop, palmtop computer, portabledigital assistant (PDA), server computer, cellular telephone, tabletcomputer, pager, combination thereof, or other computing device capableof executing instructions for performing the exemplary method.

The memory 54 may represent any type of non-transitory computer readablemedium such as random access memory (RAM), read only memory (ROM),magnetic disk or tape, optical disk, flash memory, or holographicmemory. In one embodiment, the memory 54 comprises a combination ofrandom access memory and read only memory. In some embodiments, theprocessor 58 and memory 54 may be combined in a single chip. Memory 54stores instructions for performing the exemplary method as well as theprocessed data.

The network interface 60, 64 allows the computer to communicate withother devices via a wired or wireless link, e.g., a computer network,such as a local area network (LAN) or wide area network (WAN), or theinternet, and may comprise a modulator/demodulator (MODEM), a router, acable, and/or Ethernet port.

The digital processor device 58 can be variously embodied, such as by asingle-core processor, a dual-core processor (or more generally by amultiple-core processor), a digital processor and cooperating mathco-processor, a digital controller, or the like. The digital processor58, in addition to executing instructions 56, may also control theoperation of the processing system 33.

The illustrated instructions 56 include a sensor component 66, anintensity component 68, a fractional occupancy component 70, aconcentration component 72, a movement component 74, and an outputcomponent 76.

Briefly, the sensor component 66 receives sensor data 32 from the one ormore arrays of nanostructures for each of a plurality of times (or timewindows, such as at least 5, 10, 20, or more times). The intensitycomponent 68 determines intensity data 78 for the one or more arrays ofnanostructures, based on the sensor data 32 for each of the plurality oftimes. The fractional occupancy component 70 determines fractionaloccupancy data 80 for the arrays of nanostructures, based on theintensity data 78, for each of the plurality of times. The concentrationcomponent 72 determines extracellular concentration data 82 of theanalyte, based on the fractional occupancy data 80, for each of theplurality of times.

In some particular embodiments, the system 52 comprises a localizedsurface plasmon resonance imaging (LSPRi) chip 76, which includes aglass coverslip and one or more arrays of functionalized plasmonicnanostructures patterned on the glass coverslip in contact with a fluidcontaining at least one living cell. In particular embodiments, Thesensor component 66 receives sensor data from inputs 60 such as the oneor more arrays of nanostructures on the LSPRi chip 76 for a plurality oftimes. In particular embodiments, the sensor data may comprise imagesbrightfield and/or LSPRi images of the LSPRi chip 76 taken by additionalinputs 60 such as a charge-coupled device 76.

The intensity component 68 determines intensity data for the one or morearrays of nanostructures based on the sensor data received by the sensorcomponent 66. In particular embodiments, the intensity component 68determines intensity data for each of the arrays and for each of theplurality of times. According to some embodiments, at least one of theone or more arrays is selected as a control array to be subtracted outfrom the experimental arrays. In further embodiments, the intensity datais determined by normalizing the average intensity of each of the one ormore arrays of nanostructures for a plurality of times.

The fractional occupancy component 70 determines fractional occupancydata for the one or more arrays of nanostructures based on the intensitydata determined by the intensity component 68. In particularembodiments, the fractional occupancy component 70 determines fractionaloccupancy data for each of the plurality of times. According toexemplary embodiments, a saturating amount of analyte is added to theLSPRi chip at the end of the experiment, and a relationship between theintensity data and fractional occupancy is used to determine thefractional occupancy data.

The concentration component 72 determines extracellular concentrationdata 82 for the one or more arrays of nanostructures based on thefractional occupancy data determined by the fractional occupancycomponent 70. In particular embodiments, the concentration component 72determines concentration data 82 for each of the plurality of times. Insome embodiments, the concentration component 72 subsamples thefractional occupancy data 80 over the plurality of times to determinethe concentration data 82 for each of the plurality of times. Inparticular embodiments, the concentration data 82 is determined as aprobability distribution of potential concentrations for each of the oneor more arrays of nanostructures. In exemplary embodiments, theconcentration data 82 is determined as described in the method above.

The movement component 74 determines movement data 84, which indicatesthe predicted movement of the analyte 40 in the fluid 20, based on theextracellular concentration data 82. This is achieved by mapping theextracellular concentration data for each of the one or more arrays ofnanostructures over the plurality of times to provide spatio-temporalconcentration data.

The output component 76 outputs information 86, which may include one ormore of: the concentration data 82, movement data 84, and/or informationbased thereon.

In one embodiment, the system 1 does not include a spectrometer. In thisembodiment, the sensor component 66 does not receive sensor data 32 froma spectrometer, and the intensity component 68 and fractional occupancycomponent 70 determine the intensity data and fractional occupancy datawithout data from a spectrometer. In another embodiment, the system 1may be integrated with traditional cell microscopy techniques such asfluorescence and/or brightfield imaging, which are accessible by theautomated switching of a filter cube. In some embodiments, transmittedlight imaging and/or fluorescence imaging may be performedsimultaneously with the LSPR imaging.

The term “software,” as used herein, is intended to encompass anycollection or set of instructions executable by a computer or otherdigital system so as to configure the computer or other digital systemto perform the task that is the intent of the software. The term“software” as used herein is intended to encompass such instructionsstored in storage medium such as RAM, a hard disk, optical disk, or soforth, and is also intended to encompass so-called “firmware” that issoftware stored on a ROM or so forth. Such software may be organized invarious ways, and may include software components organized aslibraries, Internet-based programs stored on a remote server or soforth, source code, interpretive code, object code, directly executablecode, and so forth. It is contemplated that the software may invokesystem-level code or calls to other software residing on a server orother location to perform certain functions.

With reference to FIG. 6, a computer-implemented method for determiningextracellular concentrations of an analyte is illustrated. The methodstarts at S100.

At S102, sensor data 32 is received by the processing system 33 from theone or more arrays 34 of functionalized plasmonic nanostructures 16. Inparticular embodiments, the sensor data may be received using a chargecoupled device 24, such as a CCD camera. In other embodiments, thesensor data may comprise additional forms of sensor data, such as sensordata from fluorescence and brightfield imaging techniques. In exemplaryembodiments, the sensor data is not received using an opticalspectrometer.

At S104, intensity data 78 for the arrays 34 of nanostructures 16 isdetermined.

At S106, fractional occupancy data 80 for the arrays 34 ofnanostructures 16 is determined based on the intensity data 78.Fractional occupancy, denoted f, represents the fraction of the arrays34 of nanostructures 16 that have an analyte 40 molecule bound to them.

At S108, extracellular concentration data 82 of the analyte isdetermined, based on the fractional occupancy data 80 of the arrays 34of nanostructures 16. In order to determine analyte concentration fromthe sensor data, the qualitative feature of array 34 brightening on theCCD camera 24 is quantified in terms of the fraction occupancy data.

Optionally, at S110, the movement of an extracellular analyte may bedetermined spatially and temporally based on the extracellularconcentration data 82. In particular embodiments, extracellularconcentration data is determined for one or more of the arrays 34 ofnanostructures 16. Based on the determined extracellular concentrationdata, the probability distributions of the concentration for each array34 may be mapped in both time and space, e.g., for a sequence of 5, 10,20, 100, or more time intervals of at least 1, 5, 10, or more seconds,or up to 100 or 1000 seconds, over a spatial range extending at least 1,10, 20, 50, or 100 μm, or more, from the center of the cell.

At S112, information is output, such as the concentration data, movementdata, information based thereon, or a combination thereof.

The method ends at S114.

The method illustrated in FIG. 6 may be implemented in a computerprogram product that may be executed on a computer. The computer programproduct may comprise a non-transitory computer-readable recording mediumon which a control program is recorded (stored), such as a disk, harddrive, or the like. Common forms of non-transitory computer-readablemedia include, for example, floppy disks, flexible disks, hard disks,magnetic tape, or any other magnetic storage medium, CD-ROM, DVD, or anyother optical medium, a RAM, a PROM, an EPROM, a FLASH-EPROM, or othermemory chip or cartridge, or any other non-transitory medium from whicha computer can read and use. The computer program product may beintegral with the computer, (for example, an internal hard drive ofRAM), or may be separate (for example, an external hard driveoperatively connected with the computer), or may be separate andaccessed via a digital data network such as a local area network (LAN)or the Internet (for example, as a redundant array of inexpensive orindependent disks (RAID) or other network server storage that isindirectly accessed by the computer, via a digital network).

Alternatively, the method may be implemented in transitory media, suchas a transmittable carrier wave in which the control program is embodiedas a data signal using transmission media, such as acoustic or lightwaves, such as those generated during radio wave and infrared datacommunications, and the like.

The exemplary method may be implemented on one or more general purposecomputers, special purpose computer(s), a programmed microprocessor ormicrocontroller and peripheral integrated circuit elements, an ASIC orother integrated circuit, a digital signal processor, a hardwiredelectronic or logic circuit such as a discrete element circuit, aprogrammable logic device such as a PLD, PLA, FPGA, Graphics card CPU(GPU), or PAL, or the like. In general, any device, capable ofimplementing a finite state machine that is in turn capable ofimplementing the flowchart shown in FIG. 6, can be used to implement themethod for determining extracellular concentrations of an analyte. Aswill be appreciated, while the steps of the method may all be computerimplemented, in some embodiments one or more of the steps may be atleast partially performed manually. As will also be appreciated, thesteps of the method need not all proceed in the order illustrated andfewer, more, or different steps may be performed.

Further details of the system and method will now be provided.

In the exemplary embodiment, image intensity data 78 is determined (atS104) based on the sensor data 32 received from the charge coupleddevice 24, without the use of a spectrometer. To determine the intensitydata 78, the mean intensity I(t), at time t of each array 34, asmeasured by the charge coupled device 24, is normalized, e g., bydividing the difference between I(t) and I₀ by a constant value toobtain a normalized intensity value at time t:I _(N)(t)=(I(t)−I ₀/(I _(f) −I ₀),

where I₀ and I_(f) are the initial and saturated array 34 intensityvalues, respectively.

When a conventional spectrometer is used, the fractional occupancy showsa non-linear relationship with image intensity making it difficult toquantify. It has been discovered, however, that there is a linearrelationship between the normalized image intensity data received fromthe sensors using a CCD camera 24 and the fractional occupancy data.Thus, it is possible to determine fractional occupancy data without theuse of a spectrometer. It has been observed that this relationship holdswhether the analyte is, for example, a 150 kDa antibody, such asanti-c-myc or 60 kDA neutravidin proteins binding to a biotinylatedsurface. However, if the CCD camera 24 has a strongwavelength-dependence on its quantum efficiency (QE) in the vicinity ofthe resonance, non-linearities tend to be introduced. The size and pitch(i.e., space between) the nanostructures 16 can be designed so that theresonance is located in a relatively flat region of the camera's 24 QEresponse while also being red-shifted from excitation wavelengths usedfor common fluorescent tags, such as GFP and red fluorescent protein(RFP).

FIG. 7 shows a plot of the normalized image intensity of a CCD camerausing the apparatus of FIG. 1 using a 400 nanostructure array of goldnanostructures with a pitch of 500 nm excited with a halogen lamp. Thesingle 20×20 array is aligned with the optical fiber.

FIG. 8 shows the normalized image intensity versus thespectrally-determined fractional occupancy obtained in three separateexperiments, illustrating the linear relationship between them.Experiments 1 and 2 use anti-c-myc monoclonal antibodies binding to ac-myc functional array in phosphate buffered saline (PBS) and serum-freemedia, respectively, and Experiment 3 uses neutravidin binding forbiotinylated nanostructures.

Fractional occupancy data 80 computed at S106 may include estimated(mean) fractional occupancy μ_(i) for an array, and its variance (e.g.,standard deviation) σ_(i), for each of M images at time t_(i), where iin an index referencing the data collected from the i-th image of Mimages, where M may be the number of arrays 34. This processed LSPRidata may be denoted D={t_(i), μ_(i), σ_(i)|i=1, . . . , M}.

In particular embodiments, the fractional occupancy data is determinedfor one or more of the arrays 34 of functionalized nanostructures 16.

Based on the fractional occupancy data, the law of mass action can beapplied to determine analyte concentration, C, using the formula:{dot over (f)}=k _(a) C·(1−f)−k _(d) f,

where {dot over (f)} is the time-derivative of the fractional occupancyμ_(i), k_(a) is the association rate constant for the functionalizednanostructures 16, and k_(d) is the disassociation rate constant for thefunctionalized nanostructures 16.

For this approach, f and {dot over (f)}, together with their relateduncertainties, are first jointly determined. In particular embodiments,the step of determining the extracellular concentration data of theanalyte includes first subsampling the fractional occupancy data using atemporal filter 42 over the plurality of times, and calculating thetime-derivative fractional occupancy data, as illustrated schematicallyin FIGS. 9-11.

With reference to FIG. 9, fractional occupancy data is plotted over aplurality of times. A time window or temporal filter 42 is shown. Thefractional occupancy data within the window is subsampled. The timewindow 42 moves along the time-axis subsampling the fractional occupancydata within each window 42. The time window 42 shown has a center attime t_(c)′, and a width h, which represents a time interval.

The time-derivative fractional occupancy may be determined based on thesubsampled fractional occupancy data. In some embodiments, one or morelocal linear models 44 are calculated for each of the instances ofsubsampling based on the time window 42. Specifically, a model meanfractional occupancy f and model mean time-derivative fractionaloccupancy {dot over (f)}, are determined, based on the local linearmodels 44 calculated for each subsample of fractional occupancy data.

FIG. 10 is an enlarged view of the samples around t_(c)′ of FIG. 9. Thevertical bars represent the standard deviation σ_(i), for eachfractional occupancy data points, μ_(i). A plurality of local linearmodels 44 that could fit the data (given the predicted deviation σ_(i))are shown for the time window 42, centered at time t_(c)′ and with awidth h.

Given the normal distribution (μ_(i), σ_(i)) for the fractionaloccupancy at each t_(i), the probability of each of the different locallinear models 44 explaining the data can be determined and a mostprobable one is selected. Each time window or temporal filter 42 gives aweight w_(i) to the subsampled data by increasing the variance of dataover the range of h. Specifically, the fractional occupancy data furtherfrom the center t_(c)′ of the time window 42 contributes less to thelocal linear models 44 than the fractional occupancy data closer to thecenter t_(c)′.

In particular embodiments, the probability of different local linearmodels fitting the data can be expressed and determined using anegative-log likelihood formula:

$L = {{{- \ln}\;{p\left( {f,{\overset{.}{f}❘t},{h;D}} \right)}} = {\sum\limits_{i = 1}^{n}\left( {{{w\left( {{t_{i}❘t},h} \right)} \cdot \frac{\left\lbrack {f + {\overset{.}{f} \cdot \left( {t_{i} - t} \right)} - \mu_{i}} \right\rbrack^{2}}{2\sigma_{i}^{2}}} + {{optionally}\mspace{14mu}{terms}\mspace{14mu}{independent}\mspace{14mu}{of}\mspace{14mu} f\mspace{14mu}{and}\mspace{14mu}\overset{.}{f}}} \right)}}$

where w(t_(i)|t, h) are the weights assigned to t_(i) by the temporalfilter 42, and i is an index referencing a plurality of data points from1 to n data points.

Various functions for w(t_(i)|t, h) defining the temporal filter 42 maybe used. In some embodiments, the functional defining the temporalfilter 42 may be a generic Gaussian profile, schematically shown as bargraphs 50 in FIG. 9. For example, the temporal filter may be given bythe equation:w(t _(i) |t,h)=e ^(−(t) ^(i) ^(−t)) ² ^(/2h) ²

where t is the center of the time window 42, and h is the width of thetime window 42.

In other embodiments, a different symmetric, location-scale function(e.g., Lorentzian, Epanechnikov) can be chosen as the filter. The chosenfunction should be positive and have a maximum value of one.

The width, h, is a free parameter that can be fixed for the entire dataset or adaptively set for each center t. The statistical property ofbias-variance tradeoff is one consideration in selecting h, because anarrow width (small h) provides a very local estimate of f and {dot over(f)} but a high variance due to the small number of noisy samples. Awider width (large h) samples more data and reduces the variance, butthe bias will increase if non-linearities in f and {dot over (f)} emergeon large time-scales.

In particular embodiments, the probability distribution, L, may bedetermined and expressed as a bivariate normal distribution with fiveparameters: f, {dot over (f)}, ρ_(xx), ρ_(xy), and ρ_(yy), wherein f and{dot over (f)} are mean model parameters determined by the local linearmodels 44, and ρ_(xx), ρ_(xy), and ρ_(yy) are the elements of theinverse of the covariance matrix.

Using Laplace's method, a Taylor series expansion of L to the secondorder at the maximum value of L may be used to express L as a bivariatenormal distribution:

${L = {{{const}.\;{+ \frac{1}{2}}}\begin{pmatrix}{f - \overset{\_}{f}} \\{\overset{.}{f} - \overset{.}{\overset{\_}{f}}}\end{pmatrix}^{T}{\sum^{- 1}\begin{pmatrix}{f - \overset{\_}{f}} \\{\overset{.}{f} - \overset{.}{\overset{\_}{f}}}\end{pmatrix}}}},{\sum^{- 1}{= {\begin{pmatrix}\sigma_{xx} & \sigma_{xy} \\\sigma_{xy} & \sigma_{yy}\end{pmatrix}^{- 1} = \begin{pmatrix}\rho_{xx} & \rho_{xy} \\\rho_{xy} & \rho_{yy}\end{pmatrix}}}}$wherein: T is the transpose, Σ is a 2-by-2 covariance matrix and the σterms are the covariance matrix elements defined by the second orderterms of the Taylor series expansion.

Taking the first derivatives of L with respect to f and {dot over (f)},and setting these to zero yields a set of equations for the location, fand {dot over (f)}, of the maximum value of L:

${\frac{\partial L}{\partial f}❘_{{f = \overset{\_}{f}},{\overset{.}{f} = \overset{.}{\overset{\_}{f}}}}} = {{\sum\limits_{i = 1}^{n}{w_{i} \cdot \frac{\overset{\_}{f} + {\overset{.}{f} \cdot \left( {t_{i} - t} \right)} - \mu_{i}}{\sigma_{i}^{2}}}} = 0}$${\frac{\partial L}{\partial\overset{.}{f}}❘_{{f = \overset{\_}{f}},{\overset{.}{f} = \overset{.}{\overset{\_}{f}}}}} = {{\sum\limits_{i = 1}^{n}{w_{i} \cdot \left( {t_{i} - t} \right) \cdot \frac{\overset{\_}{f} + {\overset{.}{\overset{\_}{f}} \cdot \left( {t_{i} - t} \right)} - \mu_{i}}{\sigma_{i}^{2}}}} = 0}$

Taking the second derivatives of L provides the equations for theinverse covariance matrix:

${\rho_{xx} = {\frac{\partial^{2}L}{\partial f^{2}} = {\sum\limits_{i = 1}^{M}\frac{w_{i}}{\sigma_{i}^{2}}}}},{\rho_{xy} = {\frac{\partial^{2}L}{{\partial f}{\partial\overset{.}{f}}} = {\sum\limits_{i = 1}^{M}{\frac{w_{i}}{\sigma_{i}^{2}} \cdot \left( {t_{i} - t} \right)}}}},{and}$$\rho_{yy} = {\frac{\partial^{2}L}{\partial{\overset{.}{f}}^{2}} = {\sum\limits_{i = 1}^{M}{\frac{w_{i}}{\sigma_{i}^{2}} \cdot \left( {t_{i} - t} \right)^{2}}}}$

In particular embodiments, because no further terms depend on f and {dotover (f)}, the parameterization of L as a bivariate normal distributionis exact for linear models.

The second derivatives can be used to re-write the previous equationsas:

${{\rho_{xx}\overset{\_}{f}} + {\rho_{xy}\overset{.}{\overset{\_}{f}}}} = \underset{\underset{\equiv a}{︸}}{\sum\limits_{i = 1}^{M}{\frac{w_{i}}{\sigma_{i}^{2}}\mu_{i}}}$${{\rho_{xy}\overset{\_}{f}} + {\rho_{yy}\overset{.}{\overset{\_}{f}}}} = \underset{\underset{\equiv b}{︸}}{\sum\limits_{i = 1}^{M}{\frac{w_{i}}{\sigma_{i}^{2}}{\mu_{i} \cdot \left( {t_{i} - t} \right)}}}$and solved to obtain:

$\overset{\_}{f} = \frac{{\rho_{yy}a} - {\rho_{xy}b}}{{\rho_{xx}\rho_{yy}} - \rho_{xy}^{2}}$and$\overset{.}{\overset{\_}{f}} = \frac{{\rho_{yy}b} - {\rho_{xy}a}}{{\rho_{xx}\rho_{yy}} - \rho_{xy}^{2}}$

where a and b are sums over the weighted mean and the weighted meantimes its time difference, respectively.

The bivariate normal probability distribution for p(f, {dot over (f)}|t,h; D) can then be expressed as:

${p\left( {f,{\overset{.}{f}❘t},{h;D}} \right)} = {\frac{\left( {{\rho_{xx}\rho_{xy}} - \rho_{xy}^{2}} \right)^{1/2}}{2\pi} \cdot {\exp\left\lbrack {{- \frac{1}{2}}\begin{pmatrix}{f - \overset{\_}{f}} \\{\overset{.}{f} - \overset{.}{\overset{\_}{f}}}\end{pmatrix}^{T}\begin{pmatrix}\rho_{xx} & \rho_{xy} \\\rho_{xy} & \rho_{yy}\end{pmatrix}\begin{pmatrix}{f - \overset{\_}{f}} \\{\overset{.}{f} - \overset{.}{\overset{\_}{f}}}\end{pmatrix}} \right\rbrack}}$

All of the parameters are therefore expressed in terms of the weights attime t, w(t_(i)|t, h), and the processed LSPRi data, D={t_(i), μ_(i),σ_(i)|=1, . . . , M}.

In particular embodiments, the extracellular concentrations of ananalyte may be determined as a probability distribution of theconcentration at time t:

${p\left( {{c❘t},{h;D}} \right)} = {\frac{1}{Z}{\int_{0}^{1}{{df}{\int_{- \infty}^{\infty}{d\overset{.}{f}{p\left( {{c❘f},\overset{.}{f}} \right)}{p\left( {f,{\overset{.}{f}❘t},{h;D}} \right)}}}}}}$

-   -   where c is a dimensionless concentration defined by c=C/K_(D),        K_(D)=k_(d)/k_(a),    -   Z is a normalization function, which may be defined by Z=∫₀        ^(∞)dc p(c|t, h; D), and    -   p(f, {dot over (f)}|t, h; D) is a bivariate normal distribution        as described above.

By integrating over the model parameters f and {dot over (f)}, theprobability distribution of the concentration c, at each time t, ofinterest can be determined, assuming a particular kinetic binding modelrepresented by p(c|f, {dot over (f)}).

The probability p(c|f, {dot over (f)}) represents the relationship ofthe fractional occupancy to the concentration and is, therefore, thecontribution from the kinetic binding model. A deterministic equationthat relates these quantities based on the Law of Mass Action can beexpressed as:

${c = {\gamma\left( {f,\overset{.}{f}} \right)}},{where}$${\gamma\left( {f,\overset{.}{f}} \right)} \equiv \frac{{k_{d}^{- 1}\overset{.}{f}} - f}{1 - f}$

Therefore, p(c|f, {dot over (f)}) can be expressed as:p(c|f,{dot over (f)})∝δ(c−γ(f,{dot over (f)}))

and the two-dimensional integral can be reduced to a line integral:

$\begin{matrix}{{p\left( {{c❘t},{h;D}} \right)} = {\frac{1}{Z}{\int_{0}^{1}{{df}{\int_{- \infty}^{\infty}{d\overset{.}{f}{\delta\left( {c - {\gamma\left( {f,\overset{.}{f}} \right)}} \right)}{p\left( {f,{\overset{.}{f}❘t},{h;D}} \right)}}}}}}} \\{= {\frac{1}{Z}\sqrt{1 + \left( {1 + c} \right)^{2}}{\int_{0}^{1}{{df}\;{p\left( {f,{{\overset{.}{f}\left( {c,f} \right)}❘t},{h;D}} \right)}}}}}\end{matrix}\quad$

where {dot over (f)} (c, f)=k_(d)c−k_(d)(1+c)·f.

Finally, the integral can be numerically determined at each time t overenough values of c to estimate the width of the probability distributionand, thus, the associated error.

The probability distribution of c, p(c|t, h; D), can be expressed as:

${p\left( {{c❘t},{h;D}} \right)} = {\frac{1}{Z\left( {t,{h;D}} \right)}{\sqrt{1 + \left( {1 + c} \right)^{2}} \cdot e^{{{- \frac{1}{2}}G} + \frac{B^{2}}{2A}}}{\int_{0}^{1}{{df}\; e^{{- \frac{A}{2}}{({f - \frac{B}{A}})}^{2}}}}}$

where the coefficients A, B, and G, are functions of the concentrationand the parameters of the bivariate normal distribution, but areindependent of f:A(c)=ρ_(xx)−2k _(d)ρ_(xy)(1+c)+k _(d) ²ρ_(yy)(1+c)²B(c)=ρ_(xx) f+k _(d)ρ_(xy)(k _(d) ⁻¹ {dot over (f)}·(1+c))−k _(d)²ρ_(yy)(k _(d) ⁻¹ {dot over (f)}−c)·(1+c)G(c)=ρ_(xx) f ²+2k _(d)ρ_(xy) f (k _(d) ⁻¹ {dot over (f)}−c)+2k _(d)²ρ_(yy)(k _(d) ⁻¹ {dot over (f)}−c)²

Each of the coefficients A, B, and G are dimensionless.

With reference to FIG. 11, this integration is illustrated. Each locallinear model 44 is a point in the f−{dot over (f)} plane 46. Allpossible local linear models 44 are summarized by the probabilitydistribution p(f, {dot over (f)}|t, h; D), a bivariate normaldistribution (depicted as elliptical contours) 48 with five parameters:the mean value (f, {dot over (f)}), and the entries (σ_(xx), σ_(xy),σ_(yy)) in the 2-by-2 covariance matrix Σ. Using the law of mass actionfor the kinetic binding model, a concentration can be assigned to eachpoint (f, {dot over (f)}). The probability of a particular concentrationc, at a time t, is determined by integrating p(f, {dot over (f)}|t, h;D) along the lines of constant concentration shown as the dashed linesradiating from the point (1, −1). The constant value for theconcentration of each line increases in the clockwise direction, andeach line integral is successively evaluated to determine p(c|t, h; D)for all c.

The Gaussian integral over the interval 0 to 1 can be solved in terms oferror functions, erf(x). In other embodiments, the integral isdetermined using numerical integration. For example, the probabilitydistribution of extracellular concentrations is solved using theintegral function in MATLAB, which employs globally adaptive quadrature.The probability distribution of the concentrations can be determined byrepeating the integral on an evenly-space logarithmic grid of values ofc ranging from 10⁻⁴ to 10⁵ for each of a plurality of times t. Forexample, the calculation may be repeated for at least 100, or at least500, or at least 1000, values of c.

In particular embodiments, the normalization function Z is computed bynon-adaptive numerical integration using only the values of c selected.

The resulting probability distributions p(c|t, h; D) may be summed oversub-intervals of c to produce confidence intervals at each time t,typically at 5% and 95% of the total probability.

Various applications of the system and method are contemplated. In aco-culture environment the label free nature of the measurements enablesabsolute concentration and concentration gradient measurements from onecell type to be correlated to the response of another, which is usefulfor determining causal relations between the secretions and cellularresponses such as motility and division. At the individual cell level,the technique can be used to identify polarized secretions useful indevelopmental biology and cell migration. In addition, the fact that thetechnique integrates with commonly used techniques in fluorescencemicroscopy allows for both label and label-free investigations of thecells. Printing applications, such as ink jet and dip-pen lithographycan be utilized to expand the functionality for multiplexingapplications capable of quantifying a variety of secreted proteins inparallel.

Without intending to limit the scope of the exemplary embodiment, thefollowing examples illustrate the application of the system and method.

EXAMPLES 1. Fabrication and Functionalization of PlasmonicNanostructures

Arrays of nanostructures were patterned onto No. 1.5 glass coverslips byspinning a bilayer resist structure consisting of polymethylmethacrylate and ethyl lactate methyl methacrylate copolymer withthicknesses of 180 nm and 250 nm respectively. The resist waselectron-beam patterned using doses of 300 μC/cm² and subsequentlydeveloped for one minute in a 2:1 solution of isopropyl alcohol:methylisobutyl ketone. A 5 nm layer of Ti followed by 70 nm of Au wasdeposited with a Temescal electron-beam evaporator. The bilayer resistwas then lifted off by soaking in acetone for 4 hours.

Radio frequency (RF) plasma ashing (40 W) with 300 mTorr of a 5%hydrogen, 95% argon mixture was used to clean the glass and goldsurfaces on the chips. The gold nanostructures were functionalized in atwo-component ethanolic-based thiol bath (0.5 mM), containing a 3:1ratio of SH—(CH₂)₈-EG₃-OH to SH—(CH₂)₁₁-EG₃-NH₂ for 18 hours, where EGstands for ethylene glycol monomer. The amine terminus was reacted witha 10 mg/mL solution of the heterobifunctional crosslinkersulfo-N-succinimidyl-4-formylbenzamide (Solulink) in phosphate-bufferedsaline (PBS) at pH 7.4, followed by a hydrazine functionalized c-mycpeptide conjugation (Solulink) in PBS buffer at pH 6.0 according to themanufacturer's instructions. For biotin-neutravidin studies, 0.3 mM ofsulfo-NHS-biotin (Thermo) in PBS was drop-coated onto the chip for 30min. Chips were rinsed with DDW and dried with nitrogen gas.Commercially available monoclonal anti-c-myc antibodies (Sigma) wereused for normalizing array response at the end of each experiment.

2. Microscopy Setup and Drift Correction

Halogen lamp light was first passed through a 594 long-pass filter andthen the Koehler illumination train of an inverted microscope (ZeissAxioObserver) before following the light path described in FIG. 1. Theobjective used was a 63×, 1.46 numerical aperture oil-immersionobjective. For spectral measurements, a 600 μm diameter optical fiberwas used to collect the scattered light from a single array and detectedwith thermoelectrically-cooled, CCD-based spectrophotometer (OceanOptics QE65000) at an integration time of 1 s. Athermoelectrically-cooled CCD camera (Hamamatsu ORCA R2) withintegration times between 200 and 250 ms was used for imagery. A heatedstage and temperature controlled enclosure kept the stage temperature at37.0±0.04° C. (Zeiss). Humidity and CO₂ were regulated at 98% and 5%,respectively, by flowing a gas-air mixture though a heated water bottleand into the enclosure. In plane drift was corrected for with imagealignment software (Zeiss Axiovision) while the focus was stabilizedusing an integrated hardware focus correction device (Zeiss DefiniteFocus).

3. Cell Culturing

Clone 9E10 Hybridoma cells (ATCC) were cultured in complete growthmedium RPMI-1640 supplemented with 10% fetal bovine serum and 1%antibiotic/antimycotic in a humidified tissue culture incubator at 37°C. under a 5% CO₂ atmosphere. Cells were maintained at a density of3-5×10⁵ cells/mL by performing passaging every two days which maintainedviability at 90-95%. Prior to LSPRi studies, the cells were pelleted bycentrifugation (900 rcf×5 min) and washed twice with RPMI-1640 SFM forthe removal of secreted antibodies and serum. For imaging, 75 μL of0.5-2×10⁶ cells/mL cell solution was manually injected into the fluidicschamber. Cell surface density was controlled by allowing cells to settleon the surface for 5 to 10 min and then microfluidically flowing SFM toremove those still in solution.

4. Data Analysis

All analysis was conducted using the Matlab 2013b environment accordingto exemplary embodiments of the methods and systems described herein.

a. Simulated Measurements

With reference to FIGS. 12-15, determination of simulated extracellularconcentration data is illustrated using the described method and systemfor receptor-ligand rate constants of k_(a)=10⁶ M⁻¹s⁻¹, k_(d)=10⁻³s⁻¹,and K_(D)=1 nM. In FIG. 12, a piece-wise function of three simulatedtime-dependent concentration scenarios is shown: a gradual increase; asharp increase; and a sharp decline. In FIG. 13, time-dependentfractional occupancy was determined by solving the equation {dot over(f)}=k_(a)C·(1−f)−k_(d)f, with added Gaussian noise typical of anexperimental setup, is shown. In FIG. 14, local linear model fits to thefractional occupancy are shown. In this simulated example, the temporalfilter is given a set width h of 270 seconds. In FIG. 15, simulatedextracellular concentration C/K_(D) is plotted over a plurality of timesaccording to one aspect of the described methods and systems. Thecircles and error bars represent the determined mode of theconcentration distribution divided by K_(D) over a 5% to 95% confidenceinterval.

Because of the relatively high association rate of the receptor-ligandpair, the slow and rapid concentration increases are faithfullyreproduced by the analysis with some curvature at the vertices due tothe filter width. The decreasing concentration step is reproduced butwith a time delay of approximately 250 seconds due to the relativelylong receptor-ligand mean binding time, 1/k_(d)=1000 seconds, whichresults in delayed sensitivity to sudden decreases in concentration.

b. Steady-State Secretions

Steady-state secretions of an analyte by several cells is quantifiedusing the described methods and systems. Anti-c-myc-secreting hybridomacells were introduced onto a LSPRi chip 12 with c-myc functionalizednanostructures 16. The density of the cells was adjusted so that thefield of view included 2 to 3 cells. At a distance of 70 μm or more fromthe cells, the secreted antibody concentration fell below the arraydetection limit (approximately 100 pM) allowing for those arrays to beused as negative controls. By having such control arrays in the samefield of view, global intensity variations, such as those due to focusdrift, could be subtracted out from the signal of arrays adjacent tocells. At the end of each experiment, a saturating solution ofcommercial anti-c-myc antibodies was introduced in order to normalizethe LSPRi intensity and calculate fractional occupancy. The kinetic rateconstants used in the analysis were determined with a commercial SPRinstrument (BioRad XPR36) using an identical surface functionalizationprotocol to that of the nanoplasmonic substrates: k_(a)=2.68×10⁴ M⁻¹s⁻¹,k_(d)=4.75×10⁻⁵ s⁻¹, and K_(D)=k_(d)/k_(a)=1.77 nM.

In FIG. 16, merged LSPRi and brightfield images showing two hybridomacells among 12 arrays of plasmonic nanostructures is shown. The localarrays, labeled Array 1 and Array 2, were used to measure the antibodyconcentration near the upper and lower cells, respectively, while theremote array, labeled Array 3, was used as a control.

In FIG. 17, the LSPRi-determined fractional occupancy is shown for array1 and array 2 after subtracting control array data from array 3. Thefractional occupancy data indicates that the lower cell was secreting ata higher rate than the upper cell.

In FIG. 18, the calculated extracellular concentration data for arrays 1and 2 are shown after applying a temporal filter with h=270 seconds. Thesymbols and error bars represent the mode of the concentrationprobability distribution divided by K_(D) with a 5% to 95% confidenceinterval. The concentration data shows a constant concentration over 40minutes, as expected for a steady-state secretion scenario, with anaverage concentration of 1.30 nM near the lower cell versus 230 pM forthe upper cell.

c. Burst Secretions

Anti-c-myc-secreting hybridoma cells were introduced onto a LSPRi chipwith c-myc functionalized nanostructures, as for the steady-statesecretion example. FIG. 19 shows merged LSPRi and brightfield imagesdisplaying a cluster of three hybridoma cells among 8 arrays. The arrayslabeled array 1 and array 2 were used to measure the concentration atvarying distances from the cell, while the array labeled array 3 wasused as a control. FIG. 20 shows the LSPRi-determined fractionaloccupancy of the three labeled arrays. FIG. 21 shows the determinedextracellular concentration for the three labeled arrays using atemporal filter with an h=45 s. The symbols and error bars represent thecalculated mode of the concentration probability distribution divided bythe K_(D) at each time point with a 5% to 95% confidence interval.

The array labeled array 1 measured a rise in fractional occupancy thatrose to 0.28 over the course of 2 minutes. This is in sharp contrastfrom the cells of FIG. 16 in which it took 40 minutes to reach a maximumfractional occupancy of 0.08. The concentration for array 1, located 24μm from the center of the three cells, peaked at 56 nM within 2 minutes.The rapid increase and decrease in concentration was best resolved usinga temporal filter with h=45 s. The secretion burst was also recorded byarray 2 located 43 μm from the center of the three cells. The peakconcentration at this array was 9 nM and time-delayed by 91 seconds fromarray 1, consistent with a burst of secreted antibodies diffusingoutwardly from the three cells.

d. Signal to Noise Versus h Value

The methods and systems described herein for determining extracellularconcentration data are adaptive in the sense that the width of thetemporal filter, as described by h, can be adjusted to best accommodatethe data. Longer h values enhance the signal to noise ratio (S/N) at theexpense of reducing the temporal resolution.

For example, with reference to FIG. 22, the determined concentration forarray 2 in FIG. 16 was plotted for h=270 s and h=150 s. Theconcentration remains the same but the error is considerably less forthe h=270 s data points. Because of the steady state nature of thesecretion, the error bars overlapped for all the data and no temporalinformation was lost by using the longer h value.

With reference to FIG. 23, the effect of varying h on the S/N ratio isshown for the determined concentrations of array 2 from FIG. 16. Ingeneral, the S/N increases linearly with increasing h values.

A comparison of the h values used in FIGS. 18 and 21 highlights thevalue of taking an adaptive approach to the determination ofextracellular concentration data. The data from FIG. 16, being steadystate in nature, can accommodate the longer h value without loss oftemporal information and take advantage of the improved signal-to-noiseratio. In FIG. 21, however, the signal-to-noise is reduced by theshorter h value but the peaks in time are readily resolved. The dynamicrange of the nanoplasmonic sensors is also highlighted by these twofigures, in which the 56 nM peak of FIG. 21 is 244-fold greater than theconcentration measured at the lower cell of FIG. 16. In general, theoptimally designed sensor will have a K_(D) value centered within therange of possible secretions.

It will be appreciated that variants of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be combined intomany other different systems or applications. Various presentlyunforeseen or unanticipated alternatives, modifications, variations orimprovements therein may be subsequently made by those skilled in theart which are also intended to be encompassed by the following claims.

What is claimed is:
 1. An imaging method for determining concentrationsof an analyte, the method comprising: forming at least one array offunctionalized plasmonic nanostructures on a localized surface plasmonresonance imaging (LSPRi) chip; contacting the at least one array with afluid comprising an analyte; illuminating the at least one array with avisible light source causing the nanostructures to emit sensor data;imaging the illuminated plasmonic nanostructures of the at least onearray with a camera for each of a plurality of times; measuringbrightness intensity data of the nanostructures for each of theplurality of times using camera imagery; determining fractionaloccupancy data for the nanostructures using the brightness intensitydata measured by the camera for each of the plurality of times sincethere is a linear relationship between intensity data from the cameraand fractional occupancy; and determining concentration data of theanalyte based on the fractional occupancy data using the law of massaction.
 2. The method of claim 1, wherein the method is performedwithout the use of a spectrometer.
 3. The method of claim 1, whereinsensor data is received from a camera positioned to receive emissionsfrom at least one of the arrays.
 4. The method of claim 1, wherein thefractional occupancy data comprises a fractional occupancy (μ_(i)) andstandard deviation (σ_(i)) determined for each of the plurality oftimes.
 5. The method of claim 1, wherein the determining of theextracellular concentration data of the analyte comprises: subsamplingthe fractional occupancy data using a temporal filter over the pluralityof times; and calculating time-derivative fractional occupancy data. 6.The method of claim 5, wherein the temporal filter has a center at atime (t) and a width (h) for each instance of subsampling over theplurality of times.
 7. The method of claim 6, wherein the temporalfilter assigns a weight (w) to the fractional occupancy data within eachinstance of subsampling over the plurality of times, based on the centerand the width of the temporal filter of that subsample.
 8. The method ofclaim 7, wherein the temporal filter assigns the weight (w) based on asymmetric, positive, location-scale function selected from a Gaussianprofile, a Lorentzian profile, and an Epanechnikov profile.
 9. Themethod of claim 5, wherein the determining of the extracellularconcentration data of the analyte further comprises: calculating atleast one local linear models with a model fractional occupancy (f) anda model time-derivative fractional occupancy ({dot over (f)}) for eachinstance of subsampling of the fractional occupancy data; anddetermining at least one probability distributions for each set of locallinear models at each instance of subsampling of the fractionaloccupancy data.
 10. The method of claim 9, wherein the probabilitydistributions are determined as a negative log likelihood that the locallinear models will fit the subsampled fractional occupancy data.
 11. Themethod of claim 9, wherein the probability distributions are determinedas a bivariate normal distribution that is exact for linear models. 12.The method of claim 9, wherein the determining of the concentration dataof the analyte further comprises calculating a probability of aconcentration of the analyte, based on the probability distributions foreach of instances of subsampling.
 13. The method of claim 1, furthercomprising determining movement of the analyte in the fluid from theconcentration data by mapping the concentration data of the analyte foreach of the at least one array of nanostructures over the plurality oftimes.
 14. The method of claim 1, wherein the method further comprisescalibrating the LSPRi chip by saturating the nanostructures with a knownconcentration of the analyte.